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Course Title: Level: Geometry Honors Grade: 8 I. Course Description/Overview This course begins with an informal introduction to geometry, experimenting with drawings, constructions, and geometry software. Using a theme of investigation before formalization, the course examines congruence, similarity, parallel and perpendicular lines, the properties of polygons and circles, perimeter and circumference, area, surface area, and volume. Students will also explore right triangle trigonometry, as well as the formulas for midpoints, distance between points, and the equation of a circle on the coordinate plane. II. Course Objectives Recognize invariants in geometric figures. Develop a literacy of mathematical proof. Derive area formulas for polygons and the surface area and volume formulas for polyhedrons. Understand how scaled figures represent mathematical similarity. Determine well defined formulas and properties of curved figures. Use right triangles and trigonometry to solve other geometric problems. Develop the fundamentals of coordinate geometry including midpoint, distance, and transformation. III. Course Content A. Introduction to Geometry Key Concepts/Skills Visualize geometric objects well enough to draw them. Use clear language to draw shapes. Distinguish between drawing a figure and constructing a figure. Use hand construction tools, including paper folding Recognize invariants and use geometry software to test for invariants Apply the Midline Conjecture Search for numerical and spatial invariants Make conjectures and use software to experiment with geometric models B. Congruence and Proof Key Concepts/Skills Develop literacy and tests pertaining to congruent figures. Identify congruent relationships that result from parallel lines cut by a transversal Write and represent a deductive proof including triangle congruence proofs Prove that the sum of the angle measures of a triangle is 180o Recognize the difference between experimentation and deduction Derive and apply the Perpendicular Bisector Theorem Apply the Isosceles Triangle Theorem to prove parts of a figure are congruent Classify quadrilaterals Understand the meaning of converse Understand the meaning of always, sometimes, and never in mathematics C. Dissections and Area Key Concepts/Skills Prove the midline theorem using cuts and rearrangement Devise and follow algorithms to dissect and rearrange a figure into an equal area figure Prove and calculate the area of a parallelogram, or a triangle, and of a trapezoid Prove the Pythagorean Theorem and use it to determine missing lengths in figures Find the surface area of solids by visualizing their nets Estimate the volumes of solids Use formulas for the volumes of certain solids D. Similarity Key Concepts/Skills Apply scale factor to make similar figures Decide whether two figures are well scaled copies of each other Use a scale factor to approximate distances in blueprints and maps Identify dilation as an enlargement or reduction by looking at the scale factor Describe the effect of the choice for center of dilation on the resulting dilation Describe and use the ratio method and the parallel line method to make dilations Decide how lines parallel to a side of a triangle split the other two sides Identify corresponding parts of similar triangles Use the AA, SAS, and SSS tests for similarity in triangles Explore the relationship in the areas of a polygon and the scaled copy of that polygon E. Circles Key Concepts/Skills Approximate the area and perimeter of irregular shapes Find the area of regular polygons Derive theorems about arcs, chords, inscribed angles, secants and tangents of circles Look for invariants in circles including the power of a point with respect to a circle Develop and apply the area and circumference formulas of a circle F. Using Similarity and a Trigonometric Introduction Key Concepts/Skills Use similar triangles to find unknown lengths Use similarity to prove theorems Use the sine, cosine, and tangent functions and their inverses to solve triangles Solve a triangle given SAS and find the area Calculate probability using a comparison of areas G. Coordinate Geometry Key Concepts/Skills Calculate the midpoint and distance of the segment given the endpoints Write equations of lines with given characteristics Apply transformations to figures and the graphs of functions in the coordinate plane IV. Types of Student Assessments and Evaluations Quizzes, tests, oral presentations, and graded homework. V. Grading Policy Grades are based on a weighted point system. Averages are calculated using a weighted system for 4 categories. Tests 40%, Quizzes 30%, Homework 15%, Other 15% (this category includes projects, presentations, graded HW, etc.) The Final exam will count for 1/9th of the overall grade for the year but will not impact the 4th marking period grade. VI. Homework Homework is given on a regular basis. Most assignments are due the next day. VII Resources Graphing calculators (TI-Nspire, TI-84, TI-83), rulers, protractors, compasses, graph paper, and text: CME Project: Geometry (CME Project Development Team) Note: This Syllabus mirrors the SHHS Geometry Syllabus. The grading policy has been adjusted for the SHMS 4 marking period -180 day course length.